In my experience getting a math degree in the US, the geometric/intuitive understanding of mathematical concepts whose absence the author laments is considered important *alongside* the axiomatic understanding.
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Mathematical education before college, and as taught in college to non-majors, definitely did suffer from lack of justification for its seemingly arbitrary rules though. They never seem to bother showing that the quadratic formula can be derived by literally drawing some squares.
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Did you mean "publicized"? The article seems to be more about teaching than publications. Anyway, mathematicians aren't blind to the fact that so many people hate math. There is no clear consensus, however, on why it happens and how to fix it.
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It's easy to blame administrations, low salaries or general anti-intellectual culture, so some people do that. The question of connection to physics and other applications gets raised too, but there is a structural problem in modern education, you have to split science into
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"genuine mathematicians do not gang up, but the weak need gangs in order to survive." You could apply this to at least one programming community as well.
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